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Quizzes > High School Quizzes > Mathematics

Commutative Property Multiplication Practice Quiz

Master Multiplication Properties with Guided Worksheet Answers

Difficulty: Moderate
Grade: Grade 3
Study OutcomesCheat Sheet
Paper art promoting The Double Property Challenge, a math quiz for middle school students.

What is the commutative property of multiplication?
a * (b * c) = (a * b) * c
a + b = b + a
a * b = a + b
a * b = b * a
The commutative property of multiplication states that changing the order of the factors does not change the product. Option A correctly shows that a multiplied by b is equal to b multiplied by a.
Which of the following correctly illustrates the commutative property using the numbers 3 and 5?
3 * 5 = 5 * 3
3 / 5 = 5 / 3
3 - 5 = 5 - 3
3 + 5 = 5 + 3
The commutative property of multiplication allows the factors to switch places without changing the product. Option A clearly demonstrates this by switching 3 and 5 in the multiplication.
If 4 * 7 = 7 * 4, which property is being demonstrated?
Commutative Property of Multiplication
Distributive Property
Associative Property of Multiplication
Identity Property
The equation 4 * 7 = 7 * 4 is a straightforward example of the commutative property of multiplication. It shows that the order of factors can be reversed without affecting the result.
What is the result of 6 * 8 and 8 * 6?
42 in both cases
48 in both cases
48 and 64
48 and 42
Thanks to the commutative property of multiplication, the product remains the same regardless of the order of the factors. Thus, both 6 * 8 and 8 * 6 equal 48.
Which statement best describes the commutative property in multiplication?
Multiplication always increases the number
In addition, the order of numbers does not matter
Division is the inverse of multiplication
In multiplication, changing the order of factors does not change the product
Option A directly explains that the commutative property of multiplication allows the factors to be rearranged without affecting the product. The other statements are either unrelated or incorrect in this context.
Which of the following options illustrates the commutative property using variables?
x + y = x * y
x * y = y * x
x * y = x + y
x + y = y + x
Option A correctly demonstrates the commutative property by showing that the order of multiplication for variables x and y can be swapped. The other options either mix operations or refer to addition.
Apply the commutative property to swap the first two factors in the expression a * b * c. Which resulting expression is correct?
a * b * c
c * a * b
b * a * c
a * c * b
Swapping the first two factors in a * b * c using the commutative property gives b * a * c. The other options involve different or no swaps, making them incorrect for this specific instruction.
Which of the following is a correct use of the commutative property in simplifying 9 * x?
9 / x
x - 9
9 + x
x * 9
The commutative property of multiplication allows the factors 9 and x to be switched, so 9 * x can be written as x * 9. The other options change the operation entirely.
If a * b = 24, which of the following using the commutative property is valid?
b * a = 24
b + a = 24
a - b = 24
a * a = 24
The commutative property allows the multiplication factors to be swapped. Therefore, if a * b = 24, then b * a must also equal 24. The other options do not reflect a valid reordering of factors.
By applying the commutative property to swap only the last two factors in 2 * 3 * 4, what is the new expression?
2 * 4 * 3
4 * 2 * 3
3 * 2 * 4
2 * 3 * 4
Swapping only the last two factors in the product 2 * 3 * 4 results in the expression 2 * 4 * 3. The other options either swap different pairs or leave the order unchanged.
Which property ensures that the order in multiplication does not affect the outcome, even with variables and numbers?
Distributive Property
Commutative Property of Multiplication
Identity Property
Associative Property
The commutative property of multiplication states that the order of factors can be interchanged without affecting the product. This rule applies equally to numerical factors and variables.
Using the commutative property, which of the following expressions is equivalent to 8 * (y * 3)?
8 * (3 * y)
8 + (3 * y)
(8 * 3) + y
3 * (8 + y)
Inside the parentheses y * 3 can be reordered to 3 * y by applying the commutative property, leaving the expression equivalent to 8 * (3 * y). The other options incorrectly change operations or structure.
Consider the equation x * 4 = 4 * x. What principle guarantees these two expressions are always equal?
Additive Inverse Property
Associative Property of Multiplication
Commutative Property of Multiplication
Identity Property
The equation x * 4 = 4 * x is a classic example of the commutative property of multiplication, which permits the factors to be interchanged. This property holds true for any numbers or variables.
If 7 * 2 = 14, what does the commutative property imply about 2 * 7?
2 * 7 = 28
2 * 7 = 21
2 * 7 = 14
2 * 7 = 9
The commutative property confirms that switching the order of factors in a multiplication does not change the product. Therefore, if 7 * 2 = 14, then 2 * 7 must also equal 14.
Which equation demonstrates the commutative property of multiplication when dealing with a constant and a variable?
5 - x = x - 5
5 / x = x / 5
5 + x = x + 5
5 * x = x * 5
The equation 5 * x = x * 5 accurately shows that the multiplication of 5 and x remains unchanged even if their order is reversed. This is a direct application of the commutative property.
Which of the following expressions correctly applies the commutative property within a larger expression: 2*(3*x) + 4?
2*(x+3) + 4
2*(3+x) + 4
2+ (x*3) + 4
2*(x*3) + 4
Option A demonstrates the correct use of the commutative property by swapping 3 and x within the parentheses. The other choices alter either the operation or the structure of the expression, leading to incorrect results.
In the expression 4 * 5 * x, a student writes it as 4 + 5 + x after applying a property. What is the error in their reasoning?
They applied the associative property incorrectly.
They used the commutative property on addition.
They confused multiplication with addition.
They performed the correct operation.
The error is that the student replaced multiplication with addition, which is not allowed under the commutative property. The commutative property only permits the rearrangement of multiplication factors, not a change in the operation.
Which of the following expressions is NOT a valid reordering of 7 * 2 * x using the commutative property?
2 * x * 7
7 * x + 2
x * 7 * 2
2 * 7 * x
The expression '7 * x + 2' is not a valid reordering because it incorrectly changes the multiplication operation to addition. The commutative property only allows the rearrangement of the factors in a multiplication.
A student claims that 10 * y = 10 + y due to the commutative property. Which statement best explains the error?
The student used the distributive property.
The commutative property requires use of different numbers.
The student incorrectly changed the operation; the commutative property does not allow addition to replace multiplication.
The student correctly applied the commutative property.
The error lies in replacing multiplication with addition, which is not permitted by the commutative property. This property only allows for reordering factors in a multiplication without altering the operation.
In a complex expression like 3*(2*(x*4)), which rearrangement correctly demonstrates applying the commutative property to the innermost multiplication?
3*(2*(x+4))
3*(2*(x*2))
3*(2*(4*x))
3*(2*(4+x))
Only Option A correctly applies the commutative property to the innermost multiplication by swapping x and 4, resulting in 4*x. The other options either change the operation or the values, which is incorrect.
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Study Outcomes

  1. Understand and explain the concept of double properties in algebra.
  2. Apply the commutative property of multiplication to simplify algebraic expressions.
  3. Analyze algebraic equations by identifying and using double properties.
  4. Evaluate and solve math problems that require the application of double properties.
  5. Demonstrate improved problem-solving skills in algebra through practice quizzes.

Multiplication Properties Cheat Sheet

  1. Commutative Property of Multiplication - The commutative property tells us that swapping factors doesn't change the product, so 3 × 4 will always equal 4 × 3. It's like arranging your books in any order and still getting the same stack height! Embrace this rule to make mental math faster and more fun. onlinemathlearning.com
  2. Using Arrays to Visualize - Arrays turn abstract numbers into friendly rows and columns, helping you see why 2 × 5 and 5 × 2 both give 10. Drawing out dots or squares reveals the commutative switcheroo in action. Give it a try next time you multiply and watch the patterns emerge. onlinemathlearning.com
  3. Real‑Life Seat Arrangements - Picture arranging chairs in a classroom: 4 rows of 6 chairs is the same total as 6 rows of 4 chairs. These everyday scenes show the commutative property at work without any complicated formulas. Next time you set the table or line up toys, spot the math hiding in plain sight. twinkl.com.pr
  4. Hands‑On Grouping - Grab some counters or blocks and split them into different groups - say, 3 groups of 7 versus 7 groups of 3. You'll always count out 21 no matter how you arrange them. This playful activity cements the idea that order doesn't matter in multiplication. twinkl.com.pr
  5. Number Line Adventures - Hop along a number line by adding or multiplying in different orders to see you land on the same spot. Whether you jump 2 then 5 or 5 then 2, you'll still reach 10. This visual journey boosts both addition and multiplication confidence. twinkl.com.pr
  6. Everyday Sharing Scenarios - Imagine sharing candies or toys: handing each friend 4 sweets five times is the same as giving them five sweets four times. Real‑world examples like snack time make abstract rules stick. Try it out with your own snack stash! twinkl.com.pr
  7. Know What Works (and What Doesn't) - Remember, only addition and multiplication are commutative - subtraction and division don't play fair when you switch order. Knowing the limits keeps you from flipping the wrong operations. Bookmark this fact for exams and quick checks! onlinemathlearning.com
  8. Worksheet Warm‑Ups - Strengthen your skills with targeted worksheets that drill the commutative property until it feels like second nature. Timed drills and fun patterns help lock in the concept. Consistency is key - daily 5‑minute practices add up! k12mathworksheets.com
  9. Song and Story Videos - Learning through catchy tunes or short stories can turn a tricky topic into a memorable adventure. Watch animated lessons that explain commutativity with characters and beats you'll hum all day. Videos are perfect for visual and auditory learners alike. onlinemathlearning.com
  10. Contextual Problem‑Solving - Test your understanding by tackling word problems that hide the commutative property in different contexts - shopping, building, or planning events. Figuring out which factors to swap boosts both comprehension and confidence. Challenge yourself with mixed drills! worksheetsgo.com
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